Additive Functional Inequalities and Partial Multipliers in Complex Banach Algebras

Jung Rye Lee (), Choonkil Park () and Themistocles M. Rassias ()
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Jung Rye Lee: Daejin University
Choonkil Park: Hanyang University
Themistocles M. Rassias: National Technical University of Athens

A chapter in Mathematical Analysis and Applications, 2019, pp 365-389 from Springer

Abstract: Abstract In this paper, we solve the additive functional inequalities 1 s a t i s h 1 ∥ f ( x + y + z ) − f ( x + y ) − f ( z ) ∥ ≤ ∥ s ( f ( x − y ) + f ( y − z ) − f ( x − z ) ) ∥ $$\displaystyle \begin{aligned} \begin{array}{rcl}{} \| f(x+y+z)-f(x+y)- f(z)\| \le \|s (f(x-y) + f(y-z )- f(x-z))\| \end{array} \end{aligned} $$ and 2 s a t i s h 2 ∥ f ( x − y ) + f ( y − z ) − f ( x − z ) ∥ ≤ ∥ s ( f ( x + y − z ) + f ( x − y + z ) − 2 f ( x ) ) ∥ , $$\displaystyle \begin{aligned} \begin{array}{rcl}{} \|f(x-y) + f(y-z )- f(x-z) \| \le \|s ( f(x+y-z) + f(x-y+z )- 2f(x) ) \| , \end{array} \end{aligned} $$ where s is a fixed nonzero complex number with |s|

Date: 2019
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DOI: 10.1007/978-3-030-31339-5_13

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